Development of layered elastic stress wave attenuators for mitigating impulsive loadings
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This research investigated the development of new material architectures for mitigating the effects of impulsive loadings, such as blast and high velocity impact, using functionally graded materials (FGM). The underlying concept explored in this research relies on stress wave attenuation associated with geometric dispersion phenomena in layered structures. The whole work presented in this dissertation can be divided into two parts. The first part focuses on the analytical study of stress wave propagation in layered structures, while the second part of the dissertation addresses optimal design of the layered structures as stress wave attenuators. For this latter part, genetic algorithms are utilized, along with the analysis procedures derived in the first part of the dissertation. The optimization involves tuning material properties and adjusting the length of each layer, along with the total length of a multilayer structure. Attenuation of elastic stress waves propagating through simple and bundled one-dimensional elastic media are investigated by considering various FGM structures situated between free and fixed surfaces. In the analytical side of this research, a transfer matrix that relates the displacement amplitudes in adjacent layers is derived in the Laplace transform domain, and then applied to analyze the layered structures. Similarly, a stress transfer function is developed for the layered structure to relate the stress output at the fixed end under any arbitrary transient load. The analytical solutions of stress at the fixed surface are obtained for Goupillaud-type media (two layers, three layers and four layers) and a two-layer structure with a large second layer. For general multilayer structures, numerical inversion of the Laplace Transform has to be employed to obtain the stress output. When an incident stress pulse passes through a layered structure, a reduced stress amplitude and elongated pulse duration can be obtained with proper selection of materials and dimensions of the layers. Consequently, an optimal design procedure is proposed to obtain the optimal FGM architecture. For the layered structures having analytical solutions, the optimal material requirement is obtained by taking into account both the stress amplitude and period; and the optimization is solved analytically. However, for general multilayer FGM structures, the optimization is focused on the stress amplitude only and solved using a real encoded adaptive genetic algorithm developed in this dissertation. By applying the load and following the procedures proposed in this dissertation, the optimal material structures for various transient loadings are achieved. The major contributions of this dissertation are three-fold: (1) The derivation of the stress transfer function relating the stress output to the applied loads for multilayer structures. (2) The derivation of analytical solutions of stress at the fixed surface for several cases of layered structures. (3) The application of real encoded adaptive genetic algorithms to generate optimal designs of the layered structures as stress wave attenuators.